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<tr><td><div id="problemNum" style='background-color:#999999;width:800;text-align:center;font-size:32px;'></div></td></tr>
<tr><td><div id="problemContent" style='word-wrap:break-word;background-color:#bbbbbb;width:800;text-align:left;font-size:Npx;'></div></td></tr>
<tr><td><div id="sum" style='word-wrap:break-word; color:#ffff22;font-size:48;background-color:#8855ff;width:800;text-align:center;'></div></td></tr>
<tr><td><div id="copyleft" style='word-wrap:break-word; color:#ffff22;font-size:18;background-color:#666666;width:800;text-align:right;'></div></td></tr>
<script language="javascript">
    //---------------------------------//
    // Project Euler 
    //
    // Author:thrombin
    //   Date:2016-05-02
    //---------------------------------//  
var p_order=21;//Problem Order
 
var problem='Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).<br/>\
If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.<br/>\
For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. <br/>\
The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.<br/>\
<br/>\
Evaluate the sum of all the amicable numbers under 10000.';
 
 
//solve the problem
//==============编程思路简介================
//  两步走：第一步求出10000以内所有数的真因子和
//          第二步逐个判断是否amicable，并求和
//=========================================
var N=10000;
var propDivs=new Array(N);
var sum=0;
 
for(var n=2;n<N;n++){
    propDivs[n]=divisorSum(n);
}
 
function divisorSum(num){
    var t_sum=1;
    for(var i=2;i<=Math.sqrt(num);i++){
        if(num%i==0){
            if(num==i*i){t_sum+=i;}
            else{t_sum+=i;t_sum+=num/i;}
        }
    }
    return t_sum;
}
for(n=2;n<N;n++){    
    if(propDivs[n]>1 && propDivs[n]<N){
        //d(a)= b, data(b)=a,并且 a！=b
        if(n==propDivs[propDivs[n]] && n!=propDivs[n])sum+=(n);
    }
}
     
 
//update browser
document.getElementById("problemNum").innerHTML="Project Euler-Problem "+p_order;
document.getElementById("problemContent").innerHTML=problem;
document.getElementById("sum").innerHTML="Answer:"+sum;
document.getElementById("copyleft").innerHTML="CopyLeft@Thrombin 2016";
</script>
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